Motion Clouds: raw principles¶

Motion Clouds are synthesized textures which aim at having similar characteristics as natural images but with controlled parameters. There are many ways to achieve these results and this notebook aims at showing that different procedures from different communities (neurioscience, modelling, computer vision, ...) may produce similar results.

In [1]:

import numpy as np
np.set_printoptions(precision=3, suppress=True)
import pylab
import matplotlib.pyplot as plt
%matplotlib inline

Using Fourier ("official Motion Clouds")¶

In [2]:

import sys
sys.path.append('..')
import MotionClouds as mc
fx, fy, ft = mc.get_grids(mc.N_X, mc.N_Y, mc.N_frame)

Using mixtures of images¶

In [3]:

import scipy.misc
lena = scipy.misc.lena() * 1.
lena -= lena.mean()
lena /= lena.std()
print lena.shape

(512, 512)

In [4]:

plt.imshow(lena, cmap=plt.cm.gray)

Out[4]:

<matplotlib.image.AxesImage at 0x11a19e810>

In [5]:

def noise(image=lena):
    for axis in [0, 1]:
        image = np.roll(image, np.random.randint(image.shape[axis]), axis=axis)
    return image

In [6]:

plt.imshow(noise(), cmap=plt.cm.gray)

Out[6]:

<matplotlib.image.AxesImage at 0x11bd08090>

In [7]:

plt.imshow(noise(), cmap=plt.cm.gray)

Out[7]:

<matplotlib.image.AxesImage at 0x11c24b190>

Using ARMA processes¶

Now, we define the ARMA process as an averaging process with a certain time constant $\tau=30.$ (in frames).

In [8]:

def ARMA(image, tau=30.):
    image = (1 - 1/tau)* image + 1/tau * noise()
    return image

initializing

In [9]:

image = ARMA(lena)
plt.imshow(image, cmap=plt.cm.gray)

Out[9]:

<matplotlib.image.AxesImage at 0x11c7808d0>

In [10]:

for _ in range(1000): image = ARMA(image)
plt.imshow(image, cmap=plt.cm.gray)

Out[10]:

<matplotlib.image.AxesImage at 0x11ccb9ed0>

In [11]:

for _ in range(1000): image = ARMA(image)
plt.imshow(image, cmap=plt.cm.gray)

Out[11]:

<matplotlib.image.AxesImage at 0x11d1fb3d0>

In [12]:

for _ in range(1000): image = ARMA(image)
plt.imshow(image, cmap=plt.cm.gray)

Out[12]:

<matplotlib.image.AxesImage at 0x11d931890>

In [16]:

%cd..
N_frame = 1024
z = np.zeros((lena.shape[0], lena.shape[1], N_frame))
z[:, :, 0] = image
for i_frame in range(1, N_frame): 
    z[:, :, i_frame] = ARMA(z[:, :, i_frame-1])
mc.anim_save(.5 + .5*z, filename='results/arma')

[51150 %] elapsed[sec]: 146.872 | ETA[sec]: -146.585

Saving sequence ../results/arma.mp4
Title: 
                      Started: 06/18/2014 17:36:44
                      Finished: 06/18/2014 17:39:11
                      Total time elapsed: 0.000 sec

In [18]:

mc.notebook = True
mc.in_show_video(name='arma')

/Users/lolo/Dropbox/science/MotionClouds
arma